Present a message upon first backtrack

src/pip/_internal/resolution/resolvelib/reporter.py

@@ -21,6 +21,11 @@ class PipReporter(BaseReporter):
         self.backtracks_by_package = defaultdict(int)  # type: DefaultDict[str, int]
 
         self._messages_at_backtrack = {
+            1: (
+                "pip is looking at multiple versions of this package to determine "
+                "which version is compatible with other requirements. "
+                "This could take a while."
+            ),
             8: (
                 "pip is looking at multiple versions of this package to determine "
                 "which version is compatible with other requirements. "

tests/functional/test_new_resolver.py

@@ -1048,7 +1048,7 @@ def test_new_resolver_prefers_installed_in_upgrade_if_latest(script):
     assert_installed(script, pkg="2")
 
 
-@pytest.mark.parametrize("N", [10, 20])
+@pytest.mark.parametrize("N", [2, 10, 20])
 def test_new_resolver_presents_messages_when_backtracking_a_lot(script, N):
     # Generate a set of wheels that will definitely cause backtracking.
     for index in range(1, N+1):
@@ -1087,7 +1087,10 @@ def test_new_resolver_presents_messages_when_backtracking_a_lot(script, N):
     )
 
     assert_installed(script, A="1.0.0", B="1.0.0", C="1.0.0")
-    if N >= 8:  # this number is hard-coded in the code too.
+    # These numbers are hard-coded in the code.
+    if N >= 1:
         assert "This could take a while." in result.stdout
-    if N >= 13:  # this number is hard-coded in the code too.
+    if N >= 8:
+        assert result.stdout.count("This could take a while.") >= 2
+    if N >= 13:
         assert "press Ctrl + C" in result.stdout